Model Development for Refining Rates in Oxygen Steelmaking: Impact and Slag-Metal Bulk Zones

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Article Model Development for Reﬁning Rates in Oxygen Steelmaking: Impact and Slag-Metal Bulk Zones

Ameya Kadrolkar * and Neslihan Dogan McMaster Steel Research Centre, Department of Materials Science and Engineering, McMaster University, Hamilton, ON L8S 4L8, Canada; [email protected] * Correspondence: [email protected]

Received: 22 December 2018; Accepted: 2 March 2019; Published: 8 March 2019

Abstract: A new approach has been adopted to predict the contribution of the impact and slag-metal bulk zones to the reﬁning rates of impurities in a top blown oxygen steelmaking process. The knowledge pertaining to the behavior of top-jets and bottom stirring plumes (water model and industrial studies) was adapted. For the impact zone, the surface renewal generated by the top jet as well as bottom stirring plumes is incorporated in the current model, whereas in the case of slag-metal bulk zones the surface renewal is caused solely by the bottom stirring plumes. This approach helped in achieving a more explicit use of process parameters in quantifying the slag formation. The results suggest a minor contribution of these two zones to the overall reﬁning of impurities throughout the oxygen blow.

Keywords: oxygen steelmaking; reﬁning kinetics; slag formation; penetration theory

1. Introduction The slag formation in oxygen steelmaking consists of oxidation reactions (Si, Mn, Fe, P) and the dissolution of flux additions such as CaO and MgO. At the start of the blow, there is rapid oxidation of Si and Mn due to thermodynamic favorability [1]. This is followed by the main decarburization period, in which a majority of the carbon removal takes place. Deo and Boom [2] claimed that [Si] > 0.05 wt % suppresses the CO formation/decarburization and the effective estimation of desiliconization rate is essential to predict the start of main decarburization period. Phosphorus removal takes place primarily within the metal droplets in the emulsion zone. With the dissolution of fluxes, the slag basicity increases and the oxides of P and Mn are reduced to a certain extent in the emulsion zone. Therefore, there is an increase in P and Mn contents in the bath in the middle of the blow and this phenomenon is termed “reversion” [2,3]. Although these reactions and their order of events are mostly understood through the sampling studies of the bath, the exact contribution of various reaction zones to these reactions has not been well understood. Most oxidation reactions are extremely favorable at high temperatures and the thermodynamic aspect of these reactions is known under oxygen steelmaking conditions. The progress of these reactions is limited by the kinetics of the refining reactions within individual zones. The path of slag evolution has been reported based on plant trials [4–8] and previous modeling attempts [9–16] in literature. Early models developed by Asai and Muchi [9] and Jalkanen et al. [10] assumed that the reactions take place in a single zone. Asai and Muchi [9] suggested that slag is formed solely on the surface of the cavity, by incorporating the absorption of oxygen and the simultaneous oxidation of carbon, silicon and manganese. The rate constants (and their relative magnitudes) for these oxidation reactions were considered as input data. The mean residence time of steel at the surface of the cavity was extremely small ~ 10−5 s, which does not reflect the actual circulation of metal underneath the cavity. Jalkanen et al. [10,11] described refining with a generalized reaction zone. They incorporated the

Metals 2019, 9, 309; doi:10.3390/met9030309 www.mdpi.com/journal/metals Metals 2019, 9, 309 2 of 22 reaction affinities and diffusivity of the impurities, and the transport of the impurities to the reaction zone due to energy dissipation from top blown and bottom stirring gases. An energy dissipation model developed by Nakanishi et al. [17] was applied. The mass transfer of impurities is correlated with top gas and bottom stirred gas flow rates by introducing two fitting parameters. Even though their approach is an effective way to describe the oxidation rate of impurities and the slag formation phenomena, an assessment of these two parameters is not available. These fitted parameters may vary from one vessel to another or with operational conditions. Therefore, it is difficult to further assess the significance of these parameters on the calculation of mass transfer rates. Since the distinct role of impact and emulsion zones as reaction zones has been established [7,8,18], there have been recent attempts to model refining reactions in these zones separately [12–16,19]. Sarkar et al. [12] assumed that a stoichiometric equivalent quantity of hot-metal to the O2 jet gets oxidized at the impact zone, which acts as a precursor for further refining in the emulsion zone. Their modeling predictions for [Si] and [Mn] did not correlate well with those reported by Cicutti et al. [4,5]. Rout et al. [13,14] presented a three zone model in which they applied a first order rate equation to predict the refining rates of Si and Mn at the impact zone. The mass transfer of impurities in the metal phase was assumed to be the rate limiting step. The mass transfer coefficient was calculated using an empirical correlation suggested by Kitamura et al. [20] which incorporated induced stirring energy (by bottom stirring gas) in the bath and geometrical parameters of the furnace. As this correlation [20] was based on measuring the oxidation rates of impurities in hot metal in contact with a layer of FeO containing slag for experimental and industrial ladles systems, the fluid flow dynamics of these systems are different from those applicable to the impact zone in an oxygen steelmaking furnace. At the impact zone intense turbulence is generated due to the impingement of the oxygen jet and there is a relatively small amount of slag in contact with the metal bath, as the slag is displaced by the O2 jet in lateral direction. Some multi-zone models [15,16] provide a reasonable approach to predict slag formation, however the details of this model are not available in open literature. Knoop et al. [15] presented a “slag-droplet model” based on the multi-component mixed transport control (MMTC) theory [21]. It was assumed that FeO is formed in the impact zone, followed by an FeO reduction with dissolved carbon in metal droplets. The refining reactions were assumed to occur in the emulsion zone, and oxygen was supplied through the formation of FeO at the impact zone. Jung et al. [16] presented a thermodynamic model to represent various phenomena on the oxygen steelmaking such as slag formation, scrap and flux dissolution. The eight phenomena were located in a bulk metal bath (1.scrap dissolution and 2.metal homogenization), impact zone (3.surface and 4.hot-spot volume) and slag (5.slag-metal bulk reaction, 6.emulsion, 7.flux dissolution, 8.slag homogenization). The kinetics associated with these phenomena were incorporated by varying the volume of reaction zones as a function of the blowing conditions. At the impact zone, only the surface oxidation of metal is assumed to occur during the soft blow period, while during the medium and hard blow period oxidation is assumed to occur at a depth beneath the impact zone. However, the criterion for a variation of reaction zone volume is unclear and the underlying empirical reactions used to determine the volume of the reaction zones were not described. Dogan et al. [19] developed a model to predict the decarburization rate at the impact and emulsion zones separately. This work was able to predict the end point carbon content of liquid metal however it does not include other important refining reactions. Further, some recent findings on the bloating behavior of droplets were not included in these models. Coley and coworkers [22–27] conducted numerous high temperature experiments using an X-ray fluoroscopy technique to quantify the nucleation, growth and escape of CO gas bubbles within droplets and the interplay between decarburization and dephosphorization kinetics of bloated droplets in steelmaking slags. They studied the effect of temperature, metal chemistry and FeO content in slag. It was concluded that the refining rates within droplets are extremely fast and the droplet generation rate is a limiting factor to extend the refining rates for the oxygen steelmaking process. Developing a comprehensive model for top blown oxygen steelmaking that incorporates and critically investigates these new findings is currently the focus of a study by the authors of this paper. The central thesis of Metals 2019, 9, 309 3 of 22 the model is that the kinetics of oxygen steelmaking is dominated by changes in the motion of iron droplets from the moment they are ejected from the surface of the metal bath to the moment they return to metal bath. The process model focusses on the refining rates of major impurities such as carbon, silicon and manganese in different reaction zones to predict the metal and slag chemistry throughout the blow. The overarching aim of the current work is to provide better knowledge on the contribution of the refining rates at the impact zone and slag-metal bulk solely based on operational parameters using a mechanistic approach. This study is an attempt to use the theoretical findings from the experimental studies to the full-scale operating conditions by minimizing the use of empirical/fitting parameters. This would make the application of the model to different steelmaking furnaces straightforward. The conceptual model developed by Dogan et al. [19,28–30] will be used in this work. This model consists of various sub-modules to describe scrap and flux dissolution, emulsion and impact zone decarburization. In this study, two reaction zones are considered, namely reactions at the impact zone and at the slag-bulk metal interface, while the contribution of other reaction zones will be described in the subsequent work. Only few studies [4,5,31] have reported the path of slag evolution using industrial data. In the current study, the measured data of Cicutti et al. [4,5] is used to analyze the importance of refining rates for an industrial practice since the slag path was described based on the steel and slag samples taken at various times of the blow.

2. Model Development The authors suggest that the reﬁning rates of impurities are controlled by the mass transfer of impurities in the metal at the gas-metal and the slag-metal interfaces. The reﬁning rate of solutes [Si, Mn] can then be calculated using the following equation.

J[X] MX kX−gm Agmρm n o W[X] = 1000 = 100 [wt % X]b − [wt % X]i−gm (1) kX−sm Asmρm + 100 [wt % X]b − [wt % X]i−sm where W[X] is the weight of solute removed (kg/s), X represents solutes such as Si and Mn in the liquid metal, J[X] is the moles of solute removed per unit time, (mol/s), MX is the molecular weight of solute, and the subscripts gm and sm represent the gas-metal and slag-metal interface, respectively. A is the contact area/interfacial area, ρm is the density of hot-metal, kX is the mass transfer coefﬁcient of solute (m/s), [wt % X]b and [wt %X]i are the solute contents in the bath and at the interface, respectively. It is assumed that all silicon and manganese brought to the impact zone (gas-metal interface) are oxidized since oxidation of these elements is highly favorable at steelmaking temperatures, and hence [wt % X]i−gm ≈ 0, whereas the interfacial equilibrium concentration at the slag-metal bulk is determined by the distribution coefﬁcient between metal and slag.

[wt % X]i−sm = LX(wt % X) (2) where [] indicates the element dissolved in iron and () indicates the compound dissolved in slag. LX is the distribution coefﬁcient of solute between metal and slag. The LSi [32] and LMn [33] values are calculated through the approach adopted by Rout et al. [13,14,34].

2.1. Description of Fluid Flow at the Impact Zone and Slag-Metal Bulk Due to Top-Oxygen Jet Figure1 schematically depicts phenomena at the impact zone of the oxygen steelmaking furnace [3,35]. The top gas jet impinging on the metal bath surface forms a cavity and causes the displacement of liquid metal and hence leads to the continuous renewal of the reaction area. The supersonic oxygen jet is obstructed by the metal bath and its velocity is reduced to impingement point velocity, uj. The jet emerges in a radially outward direction with a further reduced velocity called tangential gas velocity, ug. A fraction of jet momentum is used to generate metal droplets from the bath Metals 2019, 9, 309 4 of 22 while the residual jet momentum induces circular eddy ﬂows in the bath, which bring the elements like C, Si and Mn to the surface of the cavity. The velocity of the bath underneath the cavity surface due to top-jetsMetals 2019 is termed, 9 FOR PEER the REVIEW surface renewal velocity, ul. 4 of 22

Figure 1. FluidFigure flow1. Fluid behavior flow behavior at impact at impact zone zone by by gasgas je jett impingement. impingement. Reproduced Reproduced from [3,35], from with [3 ,35], with permission of Springer, 1980. 𝑢,𝑢,𝑢,𝑢 are vertical velocity at the impingement point, permission of Springer, 1980. uj, ug, ul, ubottom are vertical velocity at the impingement point, tangential tangential velocity of gas-jet, and surface renewal velocity of the metal bath due to oxygen jet and velocity of gas-jet, and surface renewal velocity of the metal bath due to oxygen jet and bottom stirring bottom stirring plumes, respectively. 𝑢 > 𝑢 >> 𝑢. In the current model the surface renewal velocity plumes, respectively. u > u >> u . In the current model the surface renewal velocity due to top jet due to top jet bottomj stirringg plumesl is (𝑢 +𝑢). bottom stirring plumes is (ul + ubottom). Observation of actual fluid flow behavior in oxygen steelmaking furnace is impossible due to Observationextreme conditions. of actual Sharma, fluid flowHlinka behavior and Kern in[36] oxygen observed steelmaking the flow behavior furnace of metal is due impossible to the due to interaction of an oxygen jet with a 200 lb steel bath using an X-ray adjacent to a quartz window in extreme conditions. Sharma, Hlinka and Kern [36] observed the flow behavior of metal due to the order to establish the direction of fluid flow at the jet-metal impingement point. It is important to interactionnote of that an oxygenthey didn’t jet propose with aany 200 correlation lb steel to bath predict using the velocity an X-ray of liquid adjacent using to this a quartztechnique. window in order to establishDavenport theet al. direction [37] took ofimages fluid to flow track atcirc theulation jet-metal of plastic impingement beads in water point. induced It by is importantthe to note that theyimpinging didn’t gas proposejet. The density any correlationof plastic beads to was predict equal theto the velocity water. They of liquidwere able using to observe thistechnique. liquid behavior at a rapid speed in a radially outward direction close to the surface of the bath. They Davenport et al. [37] took images to track circulation of plastic beads in water induced by the impinging found that momentum gained from the gas jet was sufficient to carry this liquid metal stream down gas jet. Theto densitythe sides and ofplastic back to the beads center. was The equal evaluation to the of the water. surface They velocity were of liquid able metal to observe is very critical liquid behavior at a rapidto speed the calculation in a radially of mass outwardtransfer coefficient. direction Even close though to previous the surface studies of [38–42] the bath. based Theyon CFD found that momentumsimulations gained provide from thethe values gasjet of surface was sufficient velocity for toa certain carry time this step, liquid a correlation metal incorporating stream down to the the effects of blowing profile of oxygen steelmaking on surface velocity is necessary. Recently Hwang sides and back to the center. The evaluation of the surface velocity of liquid metal is very critical and Irons [43] performed water modelling studies to evaluate the velocity of surface renewal of a to the calculationwater bath of due mass to the transfer impinging coefficient. gas jet. They Even measured though the previouscavity dimensions studies using [38 –high42] speed based on CFD simulationsimaging provide and local the valuesand bulk of liquid surface velocities velocity using forthe particle a certain image time velocimetry step, a correlation(PIV) technique incorporating as the effectsa of function blowing of various profile lance of oxygen heights. steelmaking They simplified on stress surface balance velocity and suggested is necessary. the following Recently Hwang correlation, and Irons [43] performed water modelling studies to evaluate the velocity of surface renewal of a water bath due to the impinging gas jet. They measured𝑢 = 𝐴𝑢 the +𝐵 cavity dimensions using high speed(3) imaging and local andwhere bulk 𝑢 and liquid 𝑢 are velocities tangential using velocities the particle of gas imageand liquid velocimetry (due to momentum (PIV) technique of top-jet), as a function of variousrespectively. lance heights. A and They B are simplified constant values. stress Upon balance employment and suggested of the assumption the following that a correlation, linear relationship exists between the impact and tangential gas velocities, i.e., 𝑢 =𝜂.𝑢 and application of local modified Froude number similarity to the Equation 3, the following correlation was obtained = + between liquid velocity and depth of cavity;ul Aug B (3) where ug and ul are tangential velocities of gas and liquid (due to momentum of top-jet), respectively. A and B are constant values. Upon employment of the assumption that a linear relationship exists between the impact and tangential gas velocities, i.e., uj = η.ug and application of local modified Metals 2019, 9, 309 5 of 22

Froude number similarity to the Equation (3), the following correlation was obtained between liquid velocity and depth of cavity; 0√ ul = A no + B (4) where no is the depth of the cavity created due to impingement of the jet on the bath surface. Based upon their experimental observation, they suggested that this correlation was valid for varying lance heights relevant to steelmaking conditions. The effect of cavity shape [43]:

d θ = tan−1 c (5) 2no

o where θ is the cavity angle ( ) and dc is the cavity diameter. The contact distance (between jet and cavity) increases as the cavity angle θ increases. This correlation is given by [43].

p ul × 100 × cosθ = (0.026 ± 0.004) × no × 100 − (0.02 ± 0.006) (6)

This correlation incorporates the cavity dimension: shape (θ) and depth no and explicitly correlates jet parameters with liquid metal velocity at the impact zone. In this study, the methodology by Dogan et al. [19] was adapted to calculate the diameter and depth of the cavity. Thus, the knowledge of cavity dimensions allows us to calculate the velocity of metal displaced underneath the cavity due to the impact of the oxygen jet.

2.2. Description of Fluid Flow at the Impact Zone and the Slag-Metal Bulk Interface Due to Bottom Stirring

Bottom stirring by gases like Ar and N2 is widely used to homogenize the metal bath in the oxygen steelmaking process [2]. As the stirring gas is introduced from the bottom of the vessel (through either porous plugs or tuyeres), gas-metal plumes are formed, and the amount of metal reaching the surface of the metal bath increases. This increases splashing and the amount of metal in contact with the oxygen jet [44–47]. Therefore, a quantification of the amount of metal being brought to the impact zone is necessary. Krishnapishrody and Irons [48] developed a correlation between various plume parameters on a fundamental basis. They characterized the gas-metal plumes using scaled parameters to evaluate the operating variables such as metal and gas velocities in plume and metal circulation rate. Since their model results were validated against a wide variety of industrial data, this model was preferred in comparison to other models [49,50], and used in the current study to quantify the amount of metal being brought to the impact zone. A brief description of the model is as follows. Non-dimensional gas flow rate Q∗ and height z∗ are defined by the following two equations, respectively. Q Q∗ = (7) g0.5 H2.5 z z∗ = (8) H The superscript * is used to indicate non-dimensional quantity. The functional relationship ∗ ∗ ∗ between the non-dimensional liquid velocity, ubottom and Q and z is given by [48]

∗ ∗ 0.32 ∗ −0.28 ubottom = 1.16 × (Q ) (z ) (9)

The actual liquid plume velocity, ubottom can be calculated using the following non-dimensional relationship: ∗ p ubottom = ubottom gH (10) In ladles, single plumes are used to increase the mass transfer between slag and metal [51–53]. Contrary to a single gas-metal plume in a ladle, the emergence of bottom stirring plumes on a free surface is more complex. Based on locations of the bottom stirring plugs the plume may emerge to Metals 2019, 9, 309 6 of 22 different locations on a free surface. In this study, the bottom stirred plug configuration is applied based on the data reported by Bertezzolo et al. [54] for the 200-t oxygen steelmaking furnace. The top view of this interaction between 8-bottom stirring plumes and a 6-holed lance for a 200-t oxygen steelmaking furnace is shown in Figure2a,b. It should be noted that the intention of this figure is a schematic diagram to represent the assumption related to the plume-cavity interaction. The fluid flow profile is not computed by the authors. The interaction of the plumes with the cavities and the slag Metals 2019, 9 FOR PEER REVIEW 6 of 22 metal bulk is characterized on the basis of the following assumptions: steelmaking furnace is shown in Figure 2a,b. It should be noted that the intention of this figure is a 1. The eight plumes are represented by a sub-sector of 45 degrees each. The downward circulating schematic diagram to represent the assumption related to the plume-cavity interaction. The fluid flow profileplumes is donot notcomputed affect theby the flow authors. beyond The their interact respectiveion of the sub-sector. plumes with the cavities and the slag 2. metalEach bulk plume is characterized has a significant on the basis momentum of the following and by assumptions: virtue of that, undergoes complete radial expansion in its subsector. This leads to surface renewal and supply of metal to the gas-metal 1. The eight plumes are represented by a sub-sector of 45 degrees each. The downward circulating interfaceplumes (cavities) do not affect and the slag-metal flow beyond interface their respective (slag-metal sub-sector. bulk). 3. 2.Since Each only plume six cavities has a significant are created momentum (by 6 holed and lance), by virtue in contrast of that, toundergoes the 8 bottom complete stirring radial plumes, the plumesexpansion are in classifiedits subsector. in two This sets, leads namely: to surface renewal and supply of metal to the gas-metal interface (cavities) and slag-metal interface (slag-metal bulk). 3.a. Since(Plume only six set cavities A) 4 Partial are created expanded (by 6 holed plumes: lanc Twoe), in plumescontrast areto the responsible 8 bottom stirring for bringing plumes, liquid themetal plumes in are contact classified with in cavity.two sets, This namely: leads to surface renewal of single cavity as shown in a. Figure(Plume2a. set A) 4 Partial expanded plumes: Two plumes are responsible for bringing liquid b. (Plumemetal setin contact B) 4 Total with expanded cavity. This plumes: leads to Each surface of the renewal plumes of causessingle cavity surface as renewalshown in of the singleFigure cavity, 2a. as shown in Figure2b b. (Plume set B) 4 Total expanded plumes: Each of the plumes causes surface renewal of the 4. The behavior of the plumes in the annular region surrounding the cavities is uniform in single cavity, as shown in Figure 2b each sub-sector.

5. 4.TheThe instantaneous behavior of dimensionthe plumes ofin thethe cavitiesannular canregion be calculatedsurrounding as the a function cavities ofis theuniform lance in parameters each sub-sector. and from that the width of the annulus is calculated. These values are used to calculate the 5. The instantaneous dimension of the cavities can be calculated as a function of the lance instantaneousparameters reﬁningand from in that the the respective width of zones. the annulus is calculated. These values are used to 6. Thecalculate metal ﬂow the instantaneous resulting from refining the in top-jet the respective and the zones. bottom stirring plumes is assumed to be 6.additive, The metal hence flow the resulting surface from renewal the top-jet velocity and is th thee bottom sum of stirring the top-jet plumes and is theassumed bottom-stirring to be surfaceadditive, renewal hence velocities. the surface renewal velocity is the sum of the top-jet and the bottom-stirring surface renewal velocities.

Figure 2. Cont.

Metals 2019, 9, 309 7 of 22

Metals 2019, 9 FOR PEER REVIEW 7 of 22

FigureFigure 2. Schematic 2. Schematic representation representation ofof thethe intera interactionction between between cavities cavities and andplumes plumes (a) Expansion (a) Expansion of of plumeplume set set A A underneath underneath cavities cavities (Side (Side view), view), (b) Expansion (b) Expansion of plume of plume set B underneath set B underneath cavities (Side cavities (Sideview).

The solid lines in the figure represent the free surfaces (cavities, slag-metal bulk and vessel wall) The solid lines in the figure represent the free surfaces (cavities, slag-metal bulk and vessel wall) whereas the dotted lines represent the plume flow profiles. The exact location of the porous plugs at whereas the dotted lines represent the plume flow profiles. The exact location of the porous plugs at the bottom is currently unknown and is based on bottom stirring configuration of the 200-t furnace the bottombeing modeled is currently in the unknown study of Bertezzolo and is based et al. on[53]. bottom stirring configuration of the 200-t furnace being modeledThe instantaneous in the study density of Bertezzolo and composition et al. [53 differences]. between upper and lower baths are quite Thepossible, instantaneous but a large densitycirculation and of compositionmetal througho differencesut the bath betweenwould reduce upper these and gradients lower baths to a are quitesignificant possible, butextent. a large A high circulation bath circulation of metal rate throughout of 126 t/min the (refer bath Appendix would reduce A) calculated these gradients in the to a significantcurrent work extent. for Aa 170–190 high bath t bath circulation indicates ratea high of tu 126rnover t/min of bath, (refer thus Appendix decreasingA) calculatedthese (density in the currentand work composition) for a 170–190 gradients t bath and indicates their effect a high on the turnover metal flow of bath,behavior thus indecreasing a relatively theseshort period (density of and composition)time. The gradients concentration and theirand temperature effect on the gradients metal flow can behavior be neglected in a relativelyunder the shortdefined period stirring of time. conditions. The concentration and temperature gradients can be neglected under the defined stirring conditions. 2.3. Determination of Mass Transfer at the Impact Zone 2.3. Determination of Mass Transfer at the Impact Zone The mass transfer coefficient, k, can be defined according to Higbie’s penetration theory [55], The mass transfer coefficient, k, can be defined according to Higbie’s penetration theory [55], 𝐷 𝑘=2×s (11) 𝜋𝑡D k = 2 × (11) πtc where 𝐷 is the diffusion coefficient of the reacting element 𝑋, 𝑡 is the residence time of the reacting element at the impact zone/reaction interface and is defined by where D is the diffusion coefficient of the reacting element X, tc is the residence time of the reacting element at the impact zone/reaction interface and is𝑙 defined by 𝑡 = (12) 𝑢 𝑢 𝑙 lc where is the velocity of surface renewal, representstc = the ‘characteristic length’ and it is the half of (12) the circumference (i.e., arc length) of the paraboloidu cavity, since the surface renewal is assumed to be symmetric about the axis of the cavity. Based on the above stated assumptions the mass transfer where u is the velocity of surface renewal, lc represents the ‘characteristic length’ and it is the half of coefficients at the impact zone and slag-metal bulk are calculated as shown in Tables 1 and 2. the circumference (i.e., arc length) of the paraboloid cavity, since the surface renewal is assumed to be symmetric about the axis of the cavity. Based on the above stated assumptions the mass transfer coefficients at the impact zone and slag-metal bulk are calculated as shown in Tables1 and2. Metals 2019, 9, 309 8 of 22

Table 1. Evaluation of mass transfer parameters at impact zone (gas-metal interface).

Characteristic Mass Transfer Plume Set Reaction Area, m2 Time of Contact, s Length, m Coefﬁcient, m/s 1 Agm q A 2 × n 1 lc−gm D cav lc−sm = × Ccavity tc = kgm = 2 × 2 (ul + ubottom) πtc A B gm ncav

where Agm = Total area of cavities (gas-metal interfacial area), (Agm/ncav) represents area of a single cavity and Ccavity = Circumference of the cavity. It should be noted that ul and ubottom are calculated using Equations (6) and (10).

Table 2. Evaluation of mass transfer parameters at slag-metal bulk (slag-metal interface).

Characteristic Length, Mass Transfer Reaction Area, m2 Time of Contact, s m Coefﬁcient, m/s q lc−sm D Asm = A − Agm lc−sm = w tc−sm = ksm = 2 × vessel annulus (ul + ubottom) πtc−sm 2 where Asm = Area of slag-metal bulk, m , wannulus = Width of annulus between cavities and wall of vessel.

The values for the diffusion coefﬁcients of Si and Mn in the liquid iron, which are determined from experimental studies [56–58] and compiled by Kawai and Shiraishi [59], are used in the current study. They range from 4 × 10−9 to 5 × 10−9 m2/s for Si (at 1550 ◦C–1725 ◦C) and 1.77 × 10−9 to 2.5 × 10−9 m2/s for Mn (at 1550 ◦C–1700 ◦C). However, another study by Grace and Derge [60] suggests that the values are ranging from 1.78 × 10−8 to 2.11 × 10−8 m2/s for Si and 8.8 × 10−9 to 1.05 × 10−8 m2/s for Mn in carbon saturated liquid iron. It is important to note that these values are one order of magnitude higher than those obtained from Calderon et al. [56], Majdic et al. [57] and Kawai et al. [58]. Since these sets of experimental values were arrived at independently, under different experimental conditions the values were used in the calculations contrary to those suggested by Grace and Derge [60].

2.4. Determination of Impact (Reaction) Area In this study, the impact zone is deﬁned as the smooth surface of the cavities formed by the supersonic jets from the lance, where the oxygen comes in contact with the metal bath. Previous studies [61–64] indicated that the cavity surface is rough, resulting in the generation of “splash sheets” [64] or “metal-bath spraying effect” [61]. However, the surface area enhancement due to splash sheet formation is difﬁcult to estimate. Therefore, surface roughness is not included in the model development. In this study, the methodology by Dogan et al. [19] was adapted to calculate the impact area as follows. The depth no and diameter dc of the cavity are calculated using the correlation developed by Koria and Lange [65], for the penetrability of impinging oxygen jets in molten pig-iron baths. They found that these parameters were mainly affected by the oxygen supply pressure, nozzle diameter and the lance height which contribute to the momentum of gas jet. The following equations are used to calculate the depth and diameter of the cavity.

P 1 0.66 = × × × 5 2 o − no 4.469 h 0.7854 10 dthPa 1.27 1 cos α 3 (13) Pa gρmh

P 1 0.282 = × × × 5 2 o − ( + ) dc 2.813 h 0.7854 10 dthPa 1.27 1 1 sin α 3 (14) Pa gρmh Metals 2019, 9, 309 9 of 22

where h is the lance height, dt is the throat diameter of lance’s nozzle, Po is the supply pressure of oxygen, Pa is the ambient pressure inside the vessel, g is the acceleration due to gravity, α is the nozzle inclination angle. Then the area of single cavity, Ac is calculated using the correlation

3 πr 2 = c 2 + 2 − 3 Metals 2019, 9 FOR PEER REVIEW Ac 2 rc 4no rc 9 of 22 (15) 6no

𝜋𝑟 r where c is the radius of the cavity. 𝐴 = (𝑟 +4𝑛) −𝑟 (15) 6𝑛 The total impact area of jets can be calculated by summation of individual cavities for multi-nozzle lances [where2]. 𝑟 is the radius of the cavity. The total impact area of jets can be calculatedn cavby summation of individual cavities for multi- nozzle lances [2]. Agm = ∑ Ac (16) c=1

The slag-metal bulk is defined by the interface𝐴 = between𝐴 the bath and slag at the annular(16) region between the cavities and the wall of the furnace. It is evaluated by subtracting the total area of cavities from the cross-sectionalThe slag-metal areabulk is of defined the vessel. by the interface between the bath and slag at the annular region Thebetween sequence the cavities of calculation and the wall for of the furnace. refining It is model evaluated atthe by subtracting impact and the slag-metaltotal area of cavities bulk zones is from the cross-sectional area of the vessel. represented in Figure3. For every time step, the data from hot metal and scrap composition such as The sequence of calculation for the refining model at the impact and slag-metal bulk zones is manganeserepresented and silicon, in Figure metal-bath 33. For every height, time step,H, lancethe data height, from hoth, metal velocity and ofscrap the composition oxygen jet such at the as impact point ujmanganeseand bottom and gassilicon, flow metal-bath rate, Qb height,with time𝐻, lance are height, taken ℎ as ,velocity inputs. of Thethe oxygen resultant jet at cavity the impact parameters point 𝑢 and bottom gas flow rate, 𝑄 with time are taken as inputs. The resultant cavity parameters and reaction areas (impact zone and slag-metal bulk) are then evaluated, followed by the calculation of the surfaceand reaction renewal areas velocities (impact zone due and to slag-metal the top-jets bulk) and are bottom-stirringthen evaluated, followed separately by the as calculation described in the previousof the section. surface The renewal mass velocities transfer due coefficients to the top-jets at and the bottom-stirring two zones are separately calculated as described using Equation in the (11) while theprevious refining section. rate atThe the mass two transfer zones iscoefficients calculated at the using two Equation zones are (1).calculated Subsequently using Equation the composition 11 while the refining rate at the two zones is calculated using Equation 1. Subsequently the composition of the bath is updated by taking into account the instantaneous bath weight Wb, melted scrap weight of the bath is updated by taking into account the instantaneous bath weight 𝑊, melted scrap weight W W sc, weight𝑊, weight of solute of solute removed removedX 𝑊and and the the sequencesequence of of calculation calculation is repeated is repeated for the for next the time next step. time step.

Figure 3.FigureSchematic 3. Schematic representation representation of of calculation calculation procedureprocedure for for refining reﬁning model. model.

Metals 2019, 9, 309 10 of 22 Metals 2019, 9 FOR PEER REVIEW 10 of 22

3. Results and Discussion

3.1. Liquid Velocity The surfacesurface renewal renewal velocities velocities at the at impactthe impact zone werezone calculated were calculated with respect with to time,respect considering to time, theconsidering instantaneous the instantaneous blowing parameters blowing for parameters the operation for the of Cicuttioperation et al. of [4Cicutti,5]. Figure et al.4 illustrates[4,5]. Figure the 4 variationillustrates of the the variation surface renewal of the velocitysurface duerenewal to the velo top-jetcity withdue respectto the totop-jet cavity with dimensions respect atto various cavity lancedimensions heights at prevalent various duringlance heights the blow. prevalent The decrease during in lancethe blow. height The decreases decrease the surfacein lance renewal height velocitydecreases and the increases surface renewal the cavity velocity depth and radius.increase Thes the decrease cavity depth in lance and height radius. would The increasedecrease the in momentumlance height transferred would increase by the oxygenthe momentum jet to the cavity,transferred which by is expected,the oxygen but jet this to increasedthe cavity, momentum which is supplyexpected, is consumedbut this increased in droplet momentum generation supply and does is notconsumed translate in into droplet an increase generation in surface and does renewal not rate.translate This into result an increase is consistent in surface with therenewal literature. rate. Th Hwangis result and is consistent Irons [43] alsowith statedthe literature. that the Hwang kinetic energyand Irons transfer [43] also (from stated the that jet tothe the kinetic bath) energy was more transfer efficient (from at the higher jet to lance the bath) heights was based more efficient on their observation.at higher lance The heights Energy based Transfer on their Index observation. (ETI) values The for Energy higher Transfer lance heights Index were(ETI)higher values thanfor higher those forlance lower heights lance were heights. higher The than ETI those is defined for lower as a ratiolance betweenheights. theThe kineticETI is defined energy ofas the a ratio bath between and the inputthe kinetic kinetic energy energy of of the the bath jet [and43]. Similarthe input observations kinetic energy were of made the jet in [43]. recent Similar study observations by Zhou et al. were[66] onmade kinetic in recent energy study dissipation by Zhou by metalet al. bath[66] andon kinetic slag in energy oxygen steelmakingdissipation by vessels. metal For bath a 100-tand oxygenslag in steelmakingoxygen steelmaking vessel theyvessels. calculated For a 100-t the ETIoxygen value steelma to decreaseking vessel by 36%, they whencalculated the lance the ETI height value was to Nm3 lowereddecrease fromby 36%, 1.6 when m to 1 the m (forlance O heightflow was rate oflowered 3.76 from). 1.6 m to 1 m (for O2 flow rate of 3.76 ). 2 t×min ×

Figure 4. Change of cavity dimensions and surfacesurface velocity at various lance heights.

The surface renewal velocitiesvelocities due to the top jet, 𝑢ul isis compared compared with with the the surface surface renewal renewal velocity velocity due to bottom stirring, 𝑢ubottom inin FigureFigure5 5.. The The velocity velocity of of the the metal metal circulation circulation duedue toto toptop jetjet variesvaries from 0.00480.0048 m/sm/s to to 0.0052 0.0052 m/s m/s and and it it is is two two orders orders of of magnitude magnitude lower lower than than the the metal metal velocity at the top of the plume (0.45(0.45 toto 0.640.64 m/s).m/s). Even Even though though th thee characterization characterization of of metal flow ﬂow is complex due to the overlap of the varyingvarying circulation patterns with respect to top-jet and plumes, this result showsshows that the plumes dominate the supply ofof metalmetal toto thethe cavitiescavities andand thethe slag-metalslag-metal bulk.bulk.

Metals 2019, 9, 309 11 of 22 Metals 2019, 9 FOR PEER REVIEW 11 of 22

Figure 5. Comparison of surface renewal velocities due to top-jet and bottom stirring, (h = lance height, m). Figure 5. Comparison of surface renewal velocities due to top-jet and bottom stirring, (h = lance height,It should m). be noted that this model predicts a large quantity of metal (~126 t/min: procedure for the calculation described in AppendixA) is circulated by the bottom stirring plumes for a 200-t oxygen It should be noted that this model predicts a large quantity of metal (~126 t/min: procedure for steelmaking furnace described by Cicutti et al. [4,5]. However, it is worth considering exactly how the calculation described in Appendix A) is circulated by the bottom stirring plumes for a 200-t much of this metal comes into contact with oxygen from the jet or the slag. oxygen steelmaking furnace described by Cicutti et al. [4,5]. However, it is worth considering exactly how3.2. Massmuch Transfer of this Coefﬁcientsmetal comes into contact with oxygen from the jet or the slag.

3.2. MassThe valuesTransfer of Coefficients mass transfer coefficients are calculated with respect to the process parameters such as lance height and bottom stirring gas flow rate. These parameters affect the cavity dimensions and the metalThe values circulated of mass coming transfer in contact coefficients with the are oxygen calculated jet. The with mass respect transfer to coefficientthe process at parameters the cavities such as lance height and bottom stirring gas flow rate. These parameters−6 affect the cavity−6 dimensions kcav, related to liquid velocity due to the top jet varies from 6.1 × 10 to 5.8 × 10 m/s from start and the metal circulated coming in contact with the oxygen jet. The mass transfer coefficient at the to end of the blow. If the contribution of both top-jet and bottom stirring plumes is considered, kgm 𝑘 6.1 × 10 5.8 × 10 cavitiesvaries from 5.77, related× 10 −to5 toliquid6.70 velocity× 10−5 m/s. due Similarly,to the topthe jet massvaries transfer from coefficient to at the slag-metal m/s frombulk duestart to to the end top of jet the varies blow. from If6.3 the× contribution10−6 to 6.5 × 10of −both6 m/s top-jet and for and a combined bottom stirring contribution plumes oftop is 𝑘 5.77 × 10 6.70 × 10 considered,jet and bottom stirring varies from plumes it varies fromto 5.94 × 10 −m/s.5 to Similarly,7.45 × 10 −the5 m/s. mass This transfer study coefficient shows that at thethe slag-metal magnitude bulk of the due mass to the transfer top jet coefficients varies from for 6.3 the × top 10 jet to is 6.5 considerably × 10 m/s lower and for than a combined combined contributioneffect of top blowingof top jet andandbottom bottom stirring.stirring Thisplumes finding it varies is consistent from 5.94 with × 10 literature to 7.45 [17 ×, 1053,67 m/s.,68]. This studyIt shows should that be notedthe magnitude that the magnitudes of the mass are transfer lower ascoefficients compared for with the those top jet reported is considerably in the literature. lower than combined effect of top blowing and bottom stirring. This finding is consistent with literature−4 The values of mass transfer coefficients which have been reported by Ohguchi et al. [21], km = 4 × 10 [17,53,67,68]. −4 m/s and ks = 2 × 10 m/s (metal and slag phase mass transfer coefficients respectively, for gas stirred massIt transfer should betweenbe noted the that two the phases). magnitudes are lower as compared with those reported in the literature. The values of mass transfer coefficients which have been reported by Ohguchi et al. [21], In Figure6, the predictions of mass transfer coefficients at impact zone, kcav from current study 𝑘are = compared 4×10 m/s with and the 𝑘 values = 2×10 calculatedm/s (metal though and Kitamuraslag phase et mass al.’s transfer [20] approach coefficients for Cicutti respectively, et al.’s forsteelmaking gas stirred operation mass transfer (wherein between the massthe two transfer phases). coefficient varies as a function of stirring energy impartedIn Figure on the 6, the bath predictions through top-jet of mass and transfer bottom coefficients stirring gas). at impact The mass zone, transfer 𝑘 from coefficients current study have arebeen compared evaluated with at two the distinctvalues calculated bottom stirring though flow Kita rates,mura namely et al.’s the [20] base approach case of 2.5for NmCicutti3/min et al.’s and steelmaking5 Nm3/min. operation If the bottom (wherein stirring the ratemass is transfer doubled, coef anficient 11% increasevaries as in a massfunction transfer of stirring coefficient energy is impartedobserved on whereas the bath in Kitamurathrough top-jet et al.’s and case bottom the increase stirring is 23%.gas). The mass increase transfer in bottom coefficients stirring have rate 3 beenwould evaluated indeed increase at two distinct the metal bottom re-circulated stirring perflow unit rates, time namely (thus the reducing base case the mixingof 2.5 Nm time)/min but and does 5 Nm3/min. If the bottom stirring rate is doubled, an 11% increase in mass transfer coefficient is observed whereas in Kitamura et al.’s case the increase is 23%. The increase in bottom stirring rate

Metals 2019, 9 FOR PEER REVIEW 12 of 22 Metals 2019, 9, 309 12 of 22 would indeed increase the metal re-circulated per unit time (thus reducing the mixing time) but does not proportionately increase the metal reaching the interface. There is a limit to the metal coming in contactnot proportionately with the interfaces increase which the metalis discussed reaching in theSection interface. 3.3. There is a limit to the metal coming in contactThe with values the interfacespredicted whichby Kitamura is discussed et al. in[20] Section are at-least 3.3. one order of magnitude higher than thoseThe predicted values predictedin the current by Kitamura study. etIn al. Kitamura [20] are at-least et al.’s one [20] order case of the magnitude decrease higher in lance than height those translatespredicted into thean currentincrease study. in momentum In Kitamura transfer et al.’s [to20 the] case bath the and decrease a corresponding in lance height increase translates in mass to an transferincrease incoefficient momentum is observed. transfer to In the the bath current and a correspondingstudy the magnitude increase inof massmass transfertransfer coefficient coefficient is decreasesobserved. due In the to currenta decrease study in lance the magnitude height as disc of massussed transfer in the previous coefficient section. decreases The dueincreased to a decrease supply ofin lancemomentum height asis expended discussed inin thedroplet previous generation section. rather The increased than agitation supply of of bath. momentum The sudden is expended rise in massin droplet transfer generation coefficients rather in than the agitationlast 2 min of of bath. the Theblow sudden is due rise to inthreefold mass transfer increase coefficients in the bottom in the stirringlast 2 min rate of (for the blowbath homogenization). is due to threefold increase in the bottom stirring rate (for bath homogenization).

(a) (b)

Figure 6. Comparison ofof metalmetal phasephase mass mass transfer transfer coefﬁcients coefficients calculated calculated by by (a )(a Current) Current model model and and (b) (correlationb) correlation obtained obtained from from the the study study of Kitamura of Kitamura et al. et[ al.20]. [20].

3.3. Effect of Lance Height and Bottom Stirring on the Metal Circulation Rate at the Interfaces As discussed in the previous section the metal ci circulatingrculating at the interfaces, MCRI, (cavities and slag-metal bulk) is calculated separately for each time step, based on the instantaneous mass transfer coefficientcoefficient and areas and is given by the following equation.equation. MCRI = 𝑘 𝐴 𝜌 +(𝑘 𝐴 𝜌 ) MCRI = kgm Agmρmetal + (ksmAsmρmetal) (17)(17) Figure 7Error! Reference source not found.a shows the variation of total metal circulating at the Figure7a shows the variation of total metal circulating at the interfaces and the instantaneous interfaces and the instantaneous lance height and bottom stirring rates. The metal circulation rate at lance height and bottom stirring rates. The metal circulation rate at interfaces (MCRI) varies between interfaces (MCRI) varies between 388 kg/min and 468 kg/min. As expected the MCRI shows a similar 388 kg/min and 468 kg/min. As expected the MCRI shows a similar dependence on the lance height dependence on the lance height as shown by the mass transfer coefficient. The bottom stirring rate as shown by the mass transfer coefficient. The bottom stirring rate affects this parameter significantly. affects this parameter significantly. The lowered lance height represents a harder blow as shown in The lowered lance height represents a harder blow as shown in Figure7b. This figure indicates that Figure 7Error! Reference source not found.b. This figure indicates that there is a marginal change as there is a marginal change as compared to the base case. On the other hand, doubling the bottom compared to the base case. On the other hand, doubling the bottom stirring rate increases the MCRI stirring rate increases the MCRI and it varies from 446 kg/min to 523 kg/min as shown in Figure7c. and it varies from 446 kg/min to 523 kg/min as shown in Figure 7.c. The cross-sectional area of the The cross-sectional area of the plume increases successively as it rises towards the top of the metal Metals 2019, 9 FOR PEER REVIEW 13 of 22 Metals 2019, 9, 309 13 of 22 plume increases successively as it rises towards the top of the metal bath. However, regardless of the bath.mode However,of emergence regardless of the plume of the on mode the offree emergence surface, the of theplume plume is able on to the circulate free surface, the metal the plume across isa ablelarger to area, circulate where the metal metal (and across consequently a larger area, the where impurities metal (and like consequentlyC, Si and Mn) the comes impurities in contact like with C, Si andoxygen Mn) from comes either in contact the jet withor FeO oxygen in slag. from either the jet or FeO in slag. It should be be noted noted that that the the un-melted un-melted scrap scrap most most likely likely interacts interacts with with the the plumes plumes depending depending on onscrap scrap dimensions. dimensions. Consequently, Consequently, fluid fluid flow flow at atthe the impact impact and and slag-metal slag-metal bulk bulk zones zones may may also be affected by the presence of un-melted scrap. However, to the best of authors’ knowledge, there is no study availableavailable forfor thethe effectseffects of of un-melted un-melted scrap scrap on on the the fluid fluid flow flow behavior behavior as as well well as as mass mass transfer transfer of solutesof solutes in thein the open open literature. literature. Therefore, Therefore, the the interaction interaction of of un-melted un-melted scrap scrap with with the the rising rising plume plume is is not considered in the current study. not considered in the current study.

Figure 7. Effect of lance height and stirring rate on me metaltal circulated at cavities and slag-metal bulk. bulk. (a) Base case case (for (for operation operation of of Cicutti Cicutti et et al., al., (b) ( bHarder) Harder blow blow i.e., i.e., consistently consistently lower lower lance lance height height (2.2 (2.2m/1.9 m/1.9 m/1.6 m/1.6 m), (c m),) Excess (c) Excess stirring stirring rate: 5 rate: m3/s 5 (0–15 m3/s min), (0–15 16.66 min), m 16.663/s (16–17 m3/s min). (16–17 min).

3.4. Reﬁning Rates at the Interface

The change in bath weight during the blow was calculated by an approach previously suggested by Dogan et al. [28,29]. This involves accounting for the instantaneous amount of scrap t ejection return freezing/melting Wsc, droplet ejected Wmd and droplet returned Wmd to the bath and metal consumed in slag formation Wox, as indicated in Equation (18)

t t−∆t t ejection return Wb = Wb + Wsc − Wmd + Wmd − Wox (18)

The change in bath and scrap masses for Cicutti et al.’s operation is shown in Figure8. There is a minor decrease in metal bath weight in the ﬁrst 2 min of the blow due to the freezing of metal

Metals 2019, 9 FOR PEER REVIEW 14 of 22

3.4. Refining Rates at the Interface The change in bath weight during the blow was calculated by an approach previously suggested by Dogan et al. [28,29]. This involves accounting for the instantaneous amount of scrap freezing/melting 𝑊, droplet ejected 𝑊 and droplet returned 𝑊 to the bath and metal consumed in slag formation 𝑊, as indicated in Equation (18)

∆ 𝑊 =𝑊 +𝑊 −𝑊 +𝑊 −𝑊 (18) Metals 2019, 9, 309 14 of 22 The change in bath and scrap masses for Cicutti et al.’s operation is shown in Figure 8. There is a minor decrease in metal bath weight in the first 2 min of the blow due to the freezing of metal on theon thesurface surface of cold of cold scrap scrap and and a corresponding a corresponding rise rise in in scrap scrap weight. weight. Subsequently Subsequently the the scrap scrap melts melts steadilysteadily and and the the bath bath weight weight increases increases linearly. linearly. There There is is a a minor minor change change in in the the bath bath weight weight after after scrap scrap isis fully fully melted. melted.

FigureFigure 8. 8. BathBath and and scrap scrap weight weight changes changes for for Cicutti Cicutti et et al.’s al.’s [4,5] [4,5] operation. operation.

FigureFigure 9 Error!compares Reference the effect source of topnot oxygenfound. compares jets and combinedthe effect of blow top (topoxygen oxygen jets and jets combined + bottom blowstirring (top plumes) oxygen on jets the + oxidationbottom stirring rates of plumes) silicon andon the manganese oxidation in rates the liquid of silicon metal and at the manganese cavities and in thethe liquid slag-metal metal bulk at the (as cavities described and inthe the slag-metal combined bulk refining (as described model inin Figurethe combined3). The refiningrefining modelmodel inpredicts Figure oxidation 3). The refining throughout model the predicts blow. Si contentoxidation in thethroughout metal is observedthe blow. to Si decrease content inin thethe early metal part is observedof the blow, to decrease primarily in due the toearly a reduction part of the in bathblow weight, primarily (due due to freezingto a reduction of metal in onbath scrap). weight During (due tothe freezing later part of ofmetal the blow,on scrap). there During is a negligible the later change part of due the to blow, an increase there is in a bathnegligible weight, change even thoughdue to anoxidation increase continues in bath weight, to occur. even A similar though trend oxidation is observed continues forrefining to occur. of A Mn similar from trend liquid is metal. observed There for is refininghardly any of Mn oxidation from liquid of silicon metal. and There manganese is hardly taking any oxidation place due of to silicon top oxygen and manganese jets. This istaking most place likely duedue to to top the factoxygen that jets. surface This renewal is most velocity likely due is very to th smalle fact and that hence surface only renewal a marginal velocity momentum is very small of the andoxygen hence jets only is transferred a marginal to momentum the bath. of the oxygen jets is transferred to the bath.

Metals 2019, 9, 309 15 of 22 Metals 2019, 9 FOR PEER REVIEW 15 of 22

Figure 9.9. Effect of top and combinedcombined blows on thethe siliconsilicon andand manganesemanganese oxidationoxidation ratesrates duringduring oxygen blow.blow.

FigureError! Reference10 compares source the predictednot found. concentrationFigure 10 compares of silicon the and predicted manganese concentration in the metal of silicon to the measuredand manganese values in reported the metal in to the the study measured of Cicutti values et al.reported [4,5]. The in the calculated study of values Cicutti are et significantlyal. [4,5]. The highercalculated than values the measured are significantly values due higher to low than refining the measured rates at values the impact due andto lo slag-metalw refining bulkrates zones.at the Theimpact value and of slag-metal product ofbulk mass zones. transfer The value coefficient of product and reaction of mass areatransfer (k ∗ coefficientA) should and be 50–100reaction times area higher(𝑘∗𝐴) ifshould the impact be 50–100 and slag-metaltimes higher bulk if the zones impact are and considered slag-metal as major bulk zones refining are zones. considered This indicates as major thatrefining the contributionzones. This indicates of these reactionthat the contribution zones is insignificant. of these reaction The authors zones are is insignificant. currently working The authors on the calculationare currently of refiningworking rates on the in othercalculation possible of reactionrefining zones. rates in It isother still importantpossible reaction to identify zones. the possibleIt is still sourcesimportant of suchto identify a low the prediction. possible Itsources is worth of such considering a low prediction. how the selection It is worth of considering diffusion coefficient how the valuesselection from of diffusion literature coefficient would affect values the refining from literatu rate predictions.re would affect The lowerthe refining diffusion rate coefficient predictions. values The bylower Grace diffusion and Derge coefficient [54] (discussed values by in SectionGrace and 2.3) Derge will affect [54] the(discussed mass transfer in Section coefficients 2.3) will to anaffect extent, the howevermass transfer the mass coefficients transfer to rates an don’textent, increase however significantly the mass andtransfer there rates is no don’t appreciable increase increase significantly in the refiningand there rates is no (the appreciable predicted increase final silicon in the content refining decreases rates (the from predicted 0.2758 wtfinal % silicon to 0.25 content wt %. decreases from 0.2758 wt % to 0.25 wt %.

Metals 2019, 9, 309 16 of 22 Metals 2019, 9 FOR PEER REVIEW 16 of 22

Figure 10. Comparison of measured and predictionspredictions forfor siliconsilicon andand manganesemanganese inin thethe liquidliquid metal.metal.

FigureFigure 1111 shows shows the the variations variations in in the the area area of of the the impact impact zone zone and and the the slag-metal slag-metal bulk bulk zone zone and and the individualthe individual contributions contributions to the to refinement the refinement of silicon. of sili Thecon. areaThe ofarea the of impact the impact zone increaseszone increases as the as lance the heightlance height decreases. decreases. Therefore, Therefore, the slag-metal the slag-metal bulk area bulk decreases. area decreases. The refining The refining rate of silicon rate of is silicon affected is proportionately.affected proportionately. The silicon The refining silicon rate refining falls between rate falls minutes between 2 andminutes 4 due 2 toand a decrease4 due to ina decrease the weight in ofthe the weight metal of bath. the metal It can bath. be inferred It can frombe inferred this figure from that this a figure change that in lancea change height in lance willvary height the will areas vary of cavitiesthe areas and of slag-metalcavities and bulk, slag-metal but this bulk, will not but significantly this will not increase significantly the refining increase in the correspondingrefining in the reactioncorresponding zones. reaction zones. AnotherAnother possiblepossible reasonreason forfor thethe lowlow predictionspredictions mightmight bebe aa smallsmall gas-metalgas-metal reactionreaction interfaceinterface whichwhich isis relatedrelated toto thethe assumptionassumption thatthat thethe cavitycavity surfacesurface isis smoothsmooth (approximately(approximately 1515 mm22).). IfIf thethe surfacesurface areaarea ofof thethe impactimpact zonezone risesrises byby aa factorfactor ofof 1010 (by(by assumingassuming roughnessroughness duedue toto splashsplash sheetsheet formation),formation), thethe correspondingcorresponding increase inin thethe siliconsilicon refiningrefining raterate isis shownshown inin FigureFigure 1212.. TheThe finalfinal siliconsilicon contentcontent goes goes down down to to 0.20 0.20 wt wt % if% the if surfacethe surface roughness roughness is considered, is considered, but it stillbut cannot it still explaincannot theexplain rapid the oxidation rapid oxidation of silicon of silicon during during the initial the init partial of part the of blow. the blow. It isworth It is worth mentioning mentioning about about the hot-modelthe hot-model study study by Koch by Koch et al. et [ 61al.]. [61]. They They conducted conducted experiments experiments which which involved involved the the blowing blowing of anof oxygenan oxygen jet onjet aon 50 a kg 50 molten kg molten Fe-C Fe-C bath bath to simulate to simulate thetop-blown the top-blown oxygen oxygen steelmaking steelmaking process. process. The generatedThe generated droplets droplets due todue “metal-bath to “metal-bath spraying” spraying” at the at cavitythe cavity were were sampled sampled at various at various points points of the of crossthe cross section section of the of metalthe metal sampler samp duringler during a blow. a blow. The The authors authors observed observed that that at any at any given given instant, instant, the dropletsthe droplets had had lower lower carbon carbon content content than than the the metal meta bath.l bath. Further Further the the “inner” “inner” droplets droplets (ejected(ejected intointo thethe jet)jet) experiencedexperienced muchmuch higherhigher decarburizationdecarburization asas comparedcompared toto thethe “outer”“outer” dropletsdroplets (ejected(ejected awayaway fromfrom jet).jet). ThisThis indicatesindicates aa possibility of significantsignificant contribution ofof decarburization andand otherother refiningrefining reactionsreactions viavia thethe gas-metalgas-metal dropletdroplet interfaceinterface ratherrather thanthan thethe smoothsmooth cavitycavity surfaces.surfaces.

Metals 2019 9 Metals 2019,, 9 ,FOR 309 PEER REVIEW 1717 of of 22 22 Metals 2019, 9 FOR PEER REVIEW 17 of 22

Figure 11. Variation of area and contribution to refining by impact and slag-metal bulk zones. FigureFigure 11. 11. VariationVariation of of area area and contribution to refini reﬁningng by impact and slag-metal bulk zones.

Figure 12. Effect of surface roughness on oxidation rate of silicon. FigureFigure 12. 12. EffectEffect of of surface surface roughness roughness on oxidation rate of silicon.

As discussed in the section above, the flow of bottom stirring plumes to the top causes the As discussed in the section above, the the flow flow of bottom stirring plumes to to the top causes the circulation of metal. Additionally there is an escape of argon bubbles through the slag-metal interface circulation of metal. Additionally Additionally there there is is an an escape escape of of argon argon bubbles bubbles through through the the slag-metal slag-metal interface interface as argon solubility in the metal is very low. During the passage of the bubble into the slag, a thin film as argon solubility inin thethe metalmetal isis veryvery low. low. During During the the passage passage of of the the bubble bubble into into the the slag, slag, a thina thin film film of of metal is carried over, and the drainage of this film causes the suspension of metal droplets in slag. ofmetal metal is carriedis carried over, over, and and the the drainage drainage of this of this film film causes causes the suspensionthe suspension of metal of metal droplets droplets in slag. in slag. This This phenomena of the passage of argon bubbles through the liquid iron-slag interface has been This phenomena of the passage of argon bubbles through the liquid iron-slag interface has been

Metals 2019, 9, 309 18 of 22 phenomena of the passage of argon bubbles through the liquid iron-slag interface has been investigated using an in situ X-ray transmission technique [69,70] as well as mathematical modelling [71]. These studies described the effect of bubble size and interfacial tension between slag-metal on the metal suspended in slag. However, the typical observed [69] mass of ejection/entrainment of metal in the slag phase was extremely low (0.0065 g/bubble for surface tension of 1.8 N/m and bubble diameter of 11.5 mm). This would entail an ejection of 2.55 kg metal/min for Cicutti et al.’s [4] bottom stirring rate of 2.5 Nm3/min. This indicates a much lower contribution of reﬁning through this mechanism.

4. Conclusions A mechanistic description of the reﬁning phenomena at the impact and the slag-metal bulk zones is presented. This description includes the role of the oxygen jets and bottom stirring plumes in bringing the metal into contact with oxygen, using independent models for each.

1. Top-blown jets appear to cause a negligible renewal of the surface at the impact zone despite their high momentum. This leads to the conclusion that this momentum is expended in the generation of droplets. 2. The bottom stirring plumes cause a significant circulation of metal (~125 tonne/min for 2.5 m3 stirring gas/min in 200-t furnace) but do not aid the refining reactions at the impact and the slag-metal bulk zones. 3. The contribution of the impact and slag-metal bulk zones appear to be negligible in the refining reactions while the emulsion zone appears to be a significant contributor to the refining reactions.

Author Contributions: Supervision, N.D.; Formulation of model, A.K. and N.D.; Review, N.D.; Editing, A.K. and N.D.; A.K. wrote the original draft of paper. Funding: This research was funded by Natural Sciences and Engineering Research Council of Canada (NSERC), project number 20007117 and the McMaster Steel Research Centre (SRC). Acknowledgments: The authors would like to thank Gordon Irons and Anand Senguttuvan for the valuable discussions regarding this work. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature

2 Ac Area of single cavity, m 2 Agm Total area of cavities/impact zone, m 2 Asm Area between bulk slag and metal bath, m Ccavity Circumference of cavity, m D Diffusion coefficient of impurity in hot-metal, m2/s dc Diameter of cavity, m dth Throat diameter of nozzle, m H Height of metal bath, m h Lance height, m moles JX Moles of solute X transferred to interface, s m k Mass transfer coefficient, s m kX−gm Mass transfer coefficient of solute X at the impact zone/gas-metal interface, s m kX−sm Mass transfer coefficient of solute X at the slag-metal interface, s LX Distribution coefficient of silicon between hot-metal and slag lc−gm Characteristic length of cavity, m lc−sm Characteristic length of slag-metal interface, m kg MCRI Metal circulating at the interfaces, min M kg X Molecular weight of solute X, mole nbse Number of bottom stirring elements i.e., number of plumes ncav Number of cavities no Depth of cavity, m Metals 2019, 9, 309 19 of 22

P kg a Ambient pressure inside vessel, m.s2 P kg o Oxygen supply pressure, m.s2 m3 Qb Bottom stirring gas ﬂow rate, s rc Radius of cavity, m t, ∆t Time instant and time step, respectively tc Residence time of an element at interface, m/s ubottom surface renewal velocity due to bottom stirring, m/s ug Tangential velocity of oxygen jet, m/s uj Velocity of oxygen jet at impact point, m/s, ul Surface renewal velocity of hot-metal due to oxygen jet, m/s 3 Vm Volume of metal circulated, m Wb Weight of metal bath, kg Wsc Weight of melted scrap, kg W[X] Weight of solute X (silicon and manganese) removed, kg/min ejection Wmd Weight of droplets ejected from the bath, kg return Wmd Weight of droplets returning to the bath, kg Wox Weight of hot metal oxidized, kg wannulus Width of annular region between cavity and vessel walls, m X Solute in hot-metal like Si or Mn α Inclination angle of the nozzle, (◦) θ Cavity angle (cavity slope), (◦) ρ kg m Density of hot-metal, m3

Appendix A The metal circulation for Cicutti et al. data is calculated as follows: For 8 bottom stirring plug. Bottom stirring gas ﬂow rate = 150 Nm3/h (for entire blow except last two minutes). Bottom stirring gas ﬂow rate, Q = 150/3600/8 = 0.005208 Nm3/s/plug.

Table A1. Process parameters.

Q, m3/s 0.005208 H (height of metal bath), m 0.89

The value of the metal circulated by the plume (bottom stirred gas) is calculated by Equations (7) through (10).

Table A2. Calculation of metal circulation by single plume.

Metal Circulated Metal Circulated by ∗ 2 Q* z* ubottom ubottom, m/s Ap, m by Plume V m, Single Plume, m3/s kg/min

0.002225 1 0.1642 0.4854 0.0773 0.0375 Vmρm = 15774.98

So total metal circulated by 8 bottom stirring plumes (MCRI) = 15774 × 8 = 126,199.8 kg/min.

References

1. Miller, T.W.; Jimenez, J.; Sharan, A.; Goldstein, D.A. The Making, Shaping and Treating of Steel, 11th ed.; Carnegie Steel Company: Pittsburgh, PA, USA, 1998. 2. Deo, B.; Boom, R. Fundamentals of Steel Making Metallurgy; Pretince Hall International: Upper Saddle River, NJ, USA, 1993. 3. Pehlke, R.D. Steelmaking—The jet age. Metall. Trans. B 1980, 11, 539–562. [CrossRef] 4. Cicutti, C.; Valdez, M.; Pérez, T.; Petroni, J.; Gomez, A.; Donayo, R.; Ferro, L. Study of slag-metal reactions in an LD-LBE converter. In Proceedings of the 6th International Conference on Molten Slags, Fluxes and Salts, Helsinki, Finland, 12–17 June 2000; p. 367. Metals 2019, 9, 309 20 of 22

5. Cicutti, C.; Valdez, M.; Pérez, T.; Donayo, R.; Petroni, J. Analysis of slag foaming during the operation of an industrial converter. Lat. Am. Appl. Res. 2002, 32, 237–240. 6. van Hoorn, A.I.; van Konynenburg, J.T.; Kreyger, P.J. Evolution of slag composition and weight during the blow. In The Role of Slag in Basic Oxygen Steelmaking Processes, McMaster Symposium on Iron and Steelmaking No.4; McMaster University: Hamilton, ON, Canada, 1976. 7. Meyer, H.W.; Porter, W.F.; Smith, G.; Szekely, J. Slag-Metal Emulsions and Their Importance in BOF Steelmaking. J. Met. 1968, 20, 35–42. [CrossRef] 8. Schoop, J.; Resch, W.; Mahn, G. Reactions Occuring During the Oxygen Top-Blown Process and The Calculation of Metallurgical Control Parameters. Ironmak. Steelmak. 1978, 2, 72–79. 9. Asai, S.; Muchi, I. Theoretical Analysis by the Use of Mathematical Model in LD Converter Operation. Trans. ISIJ 1970, 10, 250. 10. Jalkanen, H. Experiences in physicochemical modelling of oxygen converter process(BOF). Sohn Int. Symp. Adv. Process. Met. Mater. 2006, 2, 541–554. 11. Jalkanen, H.; Holappa, L. On the role of slag in the oxygen converter process. In Proceedings of the VII International Conference on Molten Slags Fluxes and Salts, Cape Town, South Africa, 25–28 January 2004; pp. 71–76. 12. Sarkar, R.; Gupta, P.; Basu, S.; Ballal, N.B. Dynamic Modeling of LD Converter Steelmaking: Reaction Modeling Using Gibbs’ Free Energy Minimization. Metall. Mater. Trans. B 2015, 46, 961–976. [CrossRef] 13. Rout, B.K.; Brooks, G.A.; Li, Z.; Rhamdhani, A. Dynamic Modeling of Oxygen Steelmaking Process: A Multi-Zone Kinetic Approach. AISTech 2017, 2017, 1315–1326. 14. Rout, B.K.; Brooks, G.A.; Li, Z.; Rhamdhani, M.A. Analysis of Desiliconization Reaction Kinetics in a BOF. AISTech 2016, 2016, 1019–1026. 15. Knoop, W.V.D.; Deo, B.; Snoijer, A.B.; Unen, G.V.; Boom, R. A Dynamic Slag-Droplet Model for the Steelmaking Process. In Proceedings of the 4th International Conference on Molten Slags and Fluxes, Sendai, Japan, 8–11 June 1992; pp. 302–307.

16. Jung, I.H.; Hudon, P.; van Ende, M.A.; Kim, W.Y. Thermodynamic Database for P2O5 Containing Slags and Its Application to the Dephosphorisaing process. AISTech Proc. 2014, 2014, 1257–1268. 17. Nakanishi, K.; Saito, K.; Nozaki, T.; Kato, Y.; Suzuki, K.; Emi, T. Physical and Metallurgical Characteristics of Combined Processes. In Proceedings of the 65th Steelmaking Conference Proceedings, Pittsburgh, PA, USA, 28–31 March 1982; pp. 101–108. 18. Price, D.J. Steelmaking: Signiﬁcance of the emulsion in carbon removal. In Proceedings of the Process Engineering of Pyrometallurgy Symposium, London, UK, 8–15 January 1974; pp. 8–15. 19. Dogan, N.; Brooks, G.A.; Rhamdhani, M.A. Comprehensive Model of Oxygen Steelmaking Part 3: Decarburization in Impact Zone. ISIJ Int. 2011, 51, 1102–1109. [CrossRef] 20. Kitamura, S.; Kitamura, T.; Shibata, K.; Mizukami, Y.; Mukawa, S.; Nakagawa, J. Effect of Stirring Energy, Temperature and Flux Composition on Hot Metal Dephosphorization Kinetics. ISIJ Int. 1991, 31, 1322–1328. [CrossRef] 21. Ohguchi, S.; Robertson, D.G.; Deo, B.; Grieveson, P.; Jeffes, J.H. Simultaneous dephosphorization and desulfurization of molten pig iron. Ironmak. Steelmak. 1984, 11, 202–213. 22. Chen, E. Kinetic study of Droplet Swelling in BOF steelmaking. Ph.D Thesis, McMaster University, Hamilton, ON, Canada, 2011. 23. Chen, E.; Coley, K.S. Kinetic study of droplet swelling in BOF steelmaking. Ironmak. Steelmak. 2010, 37, 541–545. [CrossRef] 24. Coley, K.S.; Chen, E.; Pomeroy, M. Kinetics of reaction important in oxygen steelmaking. In Proceedings of the Extraction and Processing Division Symposium on Pyrometallurgy, San Diego, CA, USA, 16–20 June 2014; pp. 289–302. 25. Pomeroy, M.D. Decarburization Kinetics of Fe-C-S Droplets in Oxygen Steelmaking Slags. Master’s Thesis, McMaster University, Hamilton, ON, Canada, 2011. 26. Gu, K.; Dogan, N.; Coley, K.S. The Inﬂuence of Sulfur on Dephosphorization Kinetics Between Bloated Metal Droplets and Slag Containing FeO. Metall. Mater. Trans. B 2017, 48, 2343–2353. [CrossRef] 27. Gu, K.; Dogan, N.; Coley, K.S. An Assessment of the General Applicability of the Relationship Between Nucleation of CO Bubbles and Mass Transfer of Phosphorus in Liquid Iron Alloys. Metall. Mater. Trans. B 2018, 49, 1119–1135. [CrossRef] Metals 2019, 9, 309 21 of 22

28. Dogan, N. Mathematical Modelling of Oxygen Steelmaking. Ph.D Thesis, Swinburne University, Hawthorn, VIC, Australia, 2011. 29. Dogan, N.; Brooks, G.A.; Rhamdhani, M.A. Comprehensive Model of Oxygen Steelmaking Part 1: Model Development and Validation. ISIJ Int. 2011, 51, 1086–1092. [CrossRef] 30. Dogan, N.; Brooks, G.A.; Rhamdhani, M.A. Comprehensive Model of Oxygen Steelmaking Part 2: Application of Bloated Droplet Theory for Decarburization in Emulsion Zone. ISIJ Int. 2011, 51, 1093–1101. [CrossRef] 31. Masui, A.; Yamada, K.; Takahashi, K. Slagmaking, Slag/metal reactions and their sites in BOF refining processes. In The Role of Slag in Basic Oxygen Steelmaking Processes, McMaster Symposium on Iron and Steelmaking No.4; McMaster University: Hamilton, ON, Canada, 1976. 32. Narita, K.; Makino, T.; Matsumoto, H.; Hikosaka, A.; Katsuda, J. Oxidation Mechanism of Silicon in Hot Metal. Tetsu-to-Hagane 1983, 69, 1722–1733. [CrossRef] 33. Suito, H.; Inoue, R. Thermodynamic Assessment of Manganese Distribution in Hot Metal and Steel. ISIJ Int. 1995, 35, 266–271. [CrossRef] 34. Rout, B.; Brooks, G.; Rhamdhani, M.A.; Li, Z.; Schrama, F.N.; Sun, J. Dynamic Model of Basic Oxygen Steelmaking Process Based on Multi-zone Reaction Kinetics: Model Derivation and Validation. Metall. Mater. Trans. B 2018, 49, 537–557. [CrossRef] 35. Simotsuma, T.; Sano, K. The Influence of Spouting by Bath Motion. Tetsu-to-Hagane 1965, 51, 1909. 36. Sharma, S.K.; Hlinka, J.W.; Kern, D.W. The Bath Circulation, Jet Penetration and High Temperature Reaction Zone in BOF Steelmaking. In Proceedings of the InOpen Hearth and Basic Oxygen Steel Conference, Pittsburgh, PA, USA, 17–20 April 1977; pp. 187–197. 37. Davenport, W.G.; Wakelin, D.; Bradshaw, A. Interaction of both bubbles and gass jets with liquids. Heat Mass Transf. Process Metall. 1967, 24, 207–245. 38. Odenthal, H.; Falkenreck, U.; Schlüter, J. CFD Simulation of Multiphase Melt Flows in Steelmaking Converters. In Proceedings of the European Conference on Computational Fluid Dynamics, Egmond aan Zee, The Netherlands, 5–8 September 2006. 39. Odenthal, H.; Kempken, J.; Schlüter, J.; Emling, W.H. Advantageous numerical simulation of the converter blowing process. Iron Steel Technol. 2007, 4, 71–89. 40. Odenthal, H. Latest Developments for the BOF Converter. In Proceedings of the 6th International Congress on the Science and Technology of Steelmaking, Beijing, China, 12–14 May 2015. 41. Li, Y.; Lou, W.T.; Zhu, M.Y. Numerical simulation of gas and liquid flow in steelmaking converter with top and bottom combined blowing. Ironmak. Steelmak. 2013, 40, 505–514. [CrossRef] 42. Ersson, M.; Höglund, L.; Tilliander, A.; Jonsson, L.; Jönsson, P. Dynamic Coupling of Computational Fluid Dynamics and Thermodynamics Software: Applied on a Top Blown Converter. ISIJ Int. 2008, 48, 147–153. [CrossRef] 43. Hwang, H.Y.; Irons, G.A. A water model study of impinging gas jets on liquid surfaces. Metall. Mater. Trans. B Process Metall. Mater. Process. Sci. 2012, 43, 302–315. [CrossRef] 44. He, Q.L.; Standish, N. A Model Study of Droplet Generation in the BOFSteelmaking. ISIJ Int. 1990, 30, 305–309. [CrossRef] 45. Luomala, M.J.; Fabritius, T.M.J.; Härkki, J.J. The Effect of Bottom Nozzle Configuration on the Bath Behaviour in the BOF. ISIJ Int. 2004, 44, 809–816. [CrossRef] 46. Maia, B.T.; Imagawa, R.K.; Tavares, R.P. Cold Model Bath Behavior Study in LD Converter With Bottom Blowing. AISTech 2016, 55, 1083–1094. 47. Maia, B.T.; Diniz, C.N.A.; Carvalho, D.A.; Souza, D.L.D.; Guimarães, J.A.; Raissa, S. TBM Tuyeres Arrangements and Flow—Comparison between BOF thyssenkrupp CSA and Cold Model. AISTech 2017, 2017, 1335–1346. 48. Krishnapisharody, K.; Irons, G.A. An Analysis of Recirculatory Flow in Gas-Stirred Ladles. Steel Res. Int. 2010, 81, 880–885. [CrossRef] 49. Sano, M.; Mori, K. Fluid Flow and Mixing Characteristics in a Gas-stirred Molten Bath. Trans. Iron Steel Inst. Jpn. 1983, 23, 169–175. [CrossRef] 50. Murthy, G.G.K.; Ghosh, A.; Mehrotra, S.P. Characterization of two-phase axisymmetric plume in a gas stirred liquid bath-A water model study. Metall. Trans. B 1988, 19, 885–892. [CrossRef] Metals 2019, 9, 309 22 of 22

51. Szekely, J.; Lehner, T.; Chang, C. Flow phenomena, mixing, and mass transfer in argon stirred ladles. Ironmak. Steelmak. 1979, 6, 285. 52. Hsiao, C.; Lehner, T. Fluid Flow in Ladles-Experimental Results. Scand. J. Metall. 1980, 9, 105–110. 53. Nakanishi, K.; Fujii, T.; Szekely, J. Possible relationship between energy dissipation and agitation in steel processing operations. Ironmak. Steelmak. 1975, 2, 193. 54. Bertezzolo, U.; Donayo, R.; Gomez, A.; Denier, G.; Stomp, H. The LBE process at Siderar. In Proceedings of the 2nd European Oxygen Steelmaking Congress, Taranto, Italy, 13–15 October 1997. 55. Higbie, R. The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. Am. Inst. Chem. Eng. 1935, 35, 36–60. 56. Calderon, F.; Sano, N. Diffusion of Mn and Si in liquid Fe over the whole range of composition. Metall. Trans. B 1971, 2, 3325. [CrossRef] 57. Majdic, A.; Graf, D.; Schenk, J. Diffusion of Si,P,S and Mn in molten Fe. Arch. für das Eisenhüttenwes 1969, 40, 627. 58. Saito, T.; Kawai, Y.; Maruya, K. Diffusion of Some Alloying Elements in Liquid Iron. Tohuku Daigaku Senk. 1960, 16, 15. 59. Kawai, Y.; Shiraishi, Y. Handbook of Physico-Chemical Properties at High Temperatures; Iron and Steel Institute of Japan: Tokyo, Japan, 1988. 60. Grace, R.; Derge, G. Diffusion of Third Elements in Liquid Iron Saturated with Carbon. Trans. Metall. Soc. 1958, 212, 331–337. 61. Koch, K.; Falkus, J.; Ralf, B. Hot model experiments of the metal bath spraying effect during the decarburization of Fe-C melts through oxygen top blowing. Steel Res. Int. 1993, 64, 15–21. [CrossRef] 62. Lee, M.; Whitney, V.; Molloy, N. Jet-liquid interaction in a steelmaking electric arc furnace. Scand. J. Metall. 2001, 30, 330–336. [CrossRef] 63. Lee, M.S.; O’Rourke, L.; Molloy, N.A. Oscillatory ﬂow in the steelmaking vessel. Scand. J. Metall. 2003, 32, 281–288. [CrossRef] 64. Sabah, S.; Brooks, G.A. Splash Distribution in Oxygen Steelmaking. Metall. Mater. Trans. B 2014, 46, 863–872. [CrossRef] 65. Koria, S.; Lange, K.W. Penetrability of impinging gas jets in molten steel bath. Steel Res. 1987, 58, 421–426. [CrossRef] 66. Zhou, X.; Ersson, M.; Zhong, L.; Jönsson, P. Numerical Simulations of the Kinetic Energy Transfer in the Bath of a BOF Converter. Metall. Mater. Trans. B Process Metall. Mater. Process. Sci. 2016, 47, 434–445. [CrossRef] 67. Koria, S. Studies of the Bath Mixing Intensity in converter Steelmaking Processes. Can. Metall. Q. 1992, 31, 105–112. [CrossRef] 68. Koria, S.; Pal, S. Experimental study of the effect of gas injection parameters on bath mixing intensity induced during steelmaking. Steel Res. 1991, 2, 47–53. [CrossRef] 69. Han, Z.; Holappa, L. Bubble Bursting Phenomenon in Gas/Metal/Slag Systems. Metall. Mater. Trans. B 2003, 34, 525–532. [CrossRef] 70. Han, Z.; Holappa, L. Mechanisms of Iron Entrainment into Slag due to Rising Gas Bubbles. ISIJ Int. 2003, 43, 292–297. [CrossRef] 71. Kobayashi, S. lron Droplet Formation Due to Bubbles Passing through Molten lron/Slag Interface. ISIJ Int. 1993, 33, 577–582. [CrossRef]

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